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This paper presents a new distributed approach for generating all primenumbers in a given interval of integers. From Eratosthenes, who elaborated thefirst prime sieve (more than 2000 years ago), to the current generation ofparallel computers, which have permitted to reach larger bounds on the intervalor to obtain previous results in a shorter time, prime numbers generation stillrepresents an attractive domain of research and plays a central role incryptography. We propose a fully distributed algorithm for finding all primesin the interval $[2\ldots, n]$, based on the \emph{wheel sieve} and the SMER(\emph{Scheduling by Multiple Edge Reversal}) multigraph dynamics. Given amultigraph $\mathcal{M}$ of arbitrary topology, having $N$ nodes, a SMER-drivensystem is defined by the number of directed edges (arcs) between any two nodesof $\mathcal{M}$, and by the global period length of all "arc reversals" in$\mathcal{M}$. The new prime number generation method inherits the distributedand parallel nature of SMER and requires at most $n + \lfloor \sqrt{n}\rfloor$time steps. The message complexity achieves at most $n\Delta_N + \lfloor\sqrt{n}\rfloor \Delta_N$, where $1\le \Delta_N\le N - 1$ is the maximalmultidegree of $\mathcal{M}$, and the maximal amount of memory space requiredper process is $\mathcal{O}(n)$ bits.

A distributed prime sieving algorithm based on Scheduling by Multiple Edge Reversal